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Boltzmann constant

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The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. It is named after the Austrian physicist Ludwig Boltzmann, who made important contributions to the theory of statistical mechanics, in which this constant plays a crucial role. Its experimentally determined value is (in SI units):

k = 1.380 6503(24) × 10-23 J K-1

The digits in parentheses are the uncertainty (standard deviation) in the last two digits of the measured value.

The universal gas constant R is simply the Boltzmann constant multiplied by Avogadro's number. The gas constant is more useful when calculating numbers of particles in moles.

Given a thermodynamic system at an absolute temperature T, the Boltzmann constant defines an energy E = kT that is, roughly speaking, the typical amount of thermal energy carried by each microscopic particle in the system. For example, an atom in a classical ideal gas has a mean kinetic energy of 1.5 kT. The energy kT associated with room temperature, 300 K (27 °C, or 80 °F), is 4.14 × 10-21 J (25.9 meV).

In statistical mechanics, the entropy S of a system is defined as the natural logarithm of Ω, the number of distinct microscopic states available to the system given the macroscopic constraints (such as a fixed total energy E):

$S = k \, \ln \Omega$

The constant of proportionality k is the Boltzmann constant. This equation, which relates the microscopic details of the system (via Ω) to its macroscopic state (via the entropy S), is the central idea of statistical mechanics.

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